The Distribution Of Trade Sizes

If trade sizes were normally distributed, most trades would cluster tightly around some average size with very few far outside it. Real markets look nothing like that: the overwhelming majority of trades are small, but a long tail of much larger trades occurs far more often than a normal distribution would predict — trade sizes are much better described by a power law or similarly fat-tailed distribution than by a bell curve.

This matters operationally because it changes how you should think about the "average" trade. With a fat tail, the mean trade size is pulled upward by rare large trades and isn't a good description of the typical trade a market maker actually sees minute to minute — the median is far more representative, and the gap between mean and median is itself informative about how skewed the flow is. It also means market impact — how much a trade moves the price — can't be modeled as linear in size across the whole range; large trades interact with liquidity very differently than a simple scaling-up of small-trade behavior would predict, which is exactly why execution algorithms slice large parent orders into many smaller child orders rather than sending one large trade at once.

The heavy tail also means that risk models built assuming normal trade-size variability will systematically underestimate how often unusually large, market-moving trades occur.